Imaginaires in analytical geometry / William B. Smith -- Our belief in axioms and the new spaces / George Bruce Halsted -- The volume of the prismoid and cylindroid / W.H. Echols -- The beginning of mathematics, II. Geometry -- W.B. Richards -- A new elementary demonstration of the pythagorean theorem / William B. Smith -- Solution of Exercises, 1, 3, 5, 6 -- Exercises 7-20.